Geodesic
Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 675-680
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $(A, T )$ be a locally A-pseudoconvex algebra over $\mathbb{R}$ or $\mathbb{C}$. We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m(T)$.
Let $(A, T )$ be a locally A-pseudoconvex algebra over $\mathbb{R}$ or $\mathbb{C}$. We define a new topology $m (T)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m(T)$.
Classification : 46H05, 46H20
Keywords: locally A-pseudoconvex algebra; locally m-pseudoconvex algebra 
@article{CMJ_2004_54_3_a9,
     author = {Abel, M. and Arhippainen, J.},
     title = {Locally m-pseudoconvex topologies on locally {A-pseudoconvex} algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {675--680},
     year = {2004},
     volume = {54},
     number = {3},
     mrnumber = {2086724},
     zbl = {1080.46518},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a9/}
}
TY  - JOUR
AU  - Abel, M.
AU  - Arhippainen, J.
TI  - Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 675
EP  - 680
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a9/
LA  - en
ID  - CMJ_2004_54_3_a9
ER  - 
%0 Journal Article
%A Abel, M.
%A Arhippainen, J.
%T Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
%J Czechoslovak Mathematical Journal
%D 2004
%P 675-680
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a9/
%G en
%F CMJ_2004_54_3_a9
Abel, M.; Arhippainen, J. Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 675-680. http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a9/

[1] M. Abel: Gelfand-Mazur Algebras, Topological Vector Spaces, Algebras and Related Areas (Hamilton, ON). Pitman Research Notes in Math. Series  316, Longman Scientific & Technical, London, 1994, pp. 116–129. | MR

[2] M. Abel and A. Kokk: Locally pseudoconvex Gelfand-Mazur algebras. Eesti Tead. Akad. Toimetised Füüs.-Mat. 37, 377–386. (Russian) | MR

[3] J. Arhippainen: On functional representation of uniformly A-convex algebras. Math. Japon. 46 (1997), 509–515. | MR | Zbl

[4] J. Arhippainen: On functional representation of commutative locally A-convex algebras. Rocky Mountain J.  Math. 30 (2000), 777–794. | DOI | MR | Zbl

[5] A. C. Cochran: Topological algebras and Mackey topologies. Proc. Amer. Math. Soc. 30 (1971), 115–119. | DOI | MR | Zbl

[6] A. C. Cochran: Representation of A-convex algebras. Proc. Amer. Math. Soc. 41 (1973), 473–479. | MR | Zbl

[7] A. C. Cochran, R.  Keown and C. R. Williams: On class of topological algebras. Pacific J.  Math. 34 (1970), 17–25. | DOI | MR

[8] T. Husain: The Open Mapping and Closed Graph Theorems in Topological Vector Spaces. Clarendon Press, Oxford, 1965. | MR | Zbl

[9] L. Oubbi: Topologies m-convexes dans les algebres A-convexes. Rend. Circ. Mat. Palermo XLI (1992), 397–406. | MR | Zbl

[10] L. Oubbi: Representation of locally convex algebras. Rev. Mat. Univ. Complut. Madrid 35 (1994), 233–244. | MR | Zbl

[11] M. Oudadess: Unité et semi-normes dans les algèbres localement convexes. Rev. Colombiana Mat. 16 (1982), 141–150. | MR | Zbl

[12] T. W. Palmer: Banach Algebras and the General Theory of $^\ast $-Algebras. Cambridge Univ. Press, New York, 1994. | Zbl

[13] L. Waelbroeck: Topological Vector Spaces and Algebras. Lecture Notes in Math.  230. Springer-Verlag, Berlin-New York, 1971. | MR